A METHOD OF CONSTRUCTION OF THE SOLUTION OF SINGULAR INTEGRAL EQUATION WITH CAUCHY KERNEL

A. B. Grigoryan

doi:10.46991/PYSU:A/2007.47.1.003

A METHOD OF CONSTRUCTION OF THE SOLUTION OF SINGULAR INTEGRAL EQUATION WITH CAUCHY KERNEL

Authors

A. B. Grigoryan Chair of Applied Mathematics, YSU, Armenia

DOI:

https://doi.org/10.46991/PYSU:A/2007.47.1.003

Keywords:

Cauchy kernel, singular integral equations, boundary-value problems

Abstract

Basing on the methods of the theory of boundary-value problems for analytic functions, the paper constructs generalized eigenfunctions of integral operator generating by Cauchy kernel in a finite interval. Further formulas for generalized integral Fourier transform by these eigenfunctions are obtained. Then the results are applied to construct solutions of singular integral equations with Cauchy kernel and constant coefficients.

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Published

2007-03-05

How to Cite

Grigoryan, A. B. (2007). A METHOD OF CONSTRUCTION OF THE SOLUTION OF SINGULAR INTEGRAL EQUATION WITH CAUCHY KERNEL. Proceedings of the YSU A: Physical and Mathematical Sciences, 41(1 (212), 3–16. https://doi.org/10.46991/PYSU:A/2007.47.1.003